IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 1, JANUARY 2014 23

Distributed Subgradient-Based Coordination ofMultiple Renewable Generators in a Microgrid

Yinliang Xu, Student Member, IEEE, Wei Zhang, Student Member, IEEE, Wenxin Liu, Member, IEEE, Xin Wang,Frank Ferrese, Member, IEEE, Chuanzhi Zang, and Haibin Yu, Member, IEEE

Abstract—For a microgrid with high renewable energy penetra-tion to work autonomously, it must maintain its own supply-de-mand balance of active power. Maximum peak power tracking al-gorithms, which emphasize high renewable energy utilization, maycause a supply-demand imbalance when the available renewablegeneration is more than demanded, especially for autonomous mi-crogrids. Currently, droop control is one of the most popular de-centralized methods for sharing active and reactive loads amongthe distributed generators. However, conventional droop controlmethods suffer from slow and oscillating dynamic response andsteady state deviations. To overcome these problems, this paperproposes a distributed subgradient-based solution to coordinatethe operations of different types of distributed renewable gener-ators in a microgrid. By controlling the utilization levels of re-newable generators, the supply-demand balance can be well main-tained and the system dynamic performance can be significantlyimproved. Simulation results demonstrate the effectiveness of theproposed control solution.

Index Terms—Distributed cooperative control, microgrid,multi-agent system, renewable generator.

ABBREVIATIONS

AGC Automatic generation control.

CB Circuit breaker.

CLC Cooperative level control.

CMS Control mode selector.

DER Distributed energy resource.

DFIG Doubly-fed induction generator.

DG Distributed generator.

GSC Grid side converter.

Manuscript received May 25, 2012; revised October 13, 2012, February25, 2013, and July 23, 2013; accepted August 29, 2013. Date of publicationSeptember 24, 2013; date of current version December 16, 2013. This workwas supported by the U.S. National Science Foundation under Grant ECCS1125776. Paper no. TPWRS-00568-2012.Y. Xu, W. Zhang, and W. Liu are with Electrical and Computer Engineering,

New Mexico State University, Las Cruces, NM 88001 USA.X. Wang is with the School of Electronic Information and Electrical Engi-

neering, Shanghai Jiao Tong University, Shanghai, China.F. Ferrese is with Naval Surface Warfare Center, Carderock Division, West

Bethesda, MD 19112 USA.C. Zang and H. Yu are with the Chinese Academy of Sciences, Shenyang

Institute of Automation, Shenyang, China.Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPWRS.2013.2281038

MAS Multi-agent system.

MLC Machine level control.

MPPT Maximum peak power tracking.

PV Photovoltaic.

RG Renewable generator.

RSC Rotor side converter.

SG Synchronous generator.

I. INTRODUCTION

A microgrid can be defined as a cluster of loads, distributedgenerators (DGs) and energy storage systems that is ser-

viced by a distribution network and can operate in both grid-connected and islanded modes. The size of a microgrid mayrange from a typical housing estate, isolated rural communities,to mixed suburban environments, academic or public communi-ties, to commercial areas, industrial sites and trading estates, ormunicipal regions [1]. The benefits of microgrids include theirincreased reliability, improved energy efficiency, reduced en-vironmental impact, and timely response to growing consumerdemand. A microgrid is a quite appealing alternative for over-coming the challenges of integrating distributed energy resourceunits, including renewable energy sources, into power systems[2].Wind and solar power are among the most promising re-

newable power supply alternatives due to their abundance,cleanness and low production cost/unit. However, the inter-mittency of wind and solar power poses new challenges tothe operation and control of microgrids, especially under highpenetration. One important issue is the power reference controlof distributed renewable generators (RGs) under dynamicweather and load conditions. The popular maximum peakpower tracking (MPPT) algorithms [3], [4] emphasize highenergy usage efficiency but may cause a supply-demand im-balance when the maximum available renewable generationsare more than demanded, especially for autonomous micro-grids. To overcome this problem, energy storage devices suchas batteries, super-capacitors and flywheels can be used toabsorb the excess energy [5]. However, if the installed energystorage device’s capacity is still insufficient, the outputs ofthe renewable generators will have to be controlled to ensurethe supply-demand balance. Even if sufficient energy storagedevices are available, their effectiveness is limited by themaximum charging and discharging rate and charging level.

0885-8950 © 2013 IEEE

24 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 1, JANUARY 2014

For an autonomousmicrogrid, the control issues are very sim-ilar to those of large-scale power systems, such as supply-de-mand balance and frequency regulation. Due to the similarity,most existing ideas on traditional power system operation canbe introduced to small scale autonomous microgrids. In [6], theauthors propose a two-level control scheme for a wind farm,which consists of supervisory and machine levels of control. Inthis scheme, the supervisory control level decides the active andreactive power set points for all doubly-fed induction genera-tors (DFIGs), while the machine control level ensures that theset points are reached. In [7], the authors propose an optimaldispatch control strategy for a wind farm. The DFIGs were con-trolled to adjust the active and reactive power generation ac-cording to the request of the system’s central operator. In [8],the authors present a control approach for a wind farm to pro-vide a sufficient generating margin upon the request of supervi-sory controllers. In [9], the authors present a coordinated con-trol method for leveling photovoltaic (PV) generation. This con-trol scheme uses fuzzy reasoning to generate the central levelinggeneration commands to reduce the frequency deviation of theisolated power utility.All of these methods are centralized, therefore requiring

complicated communication networks to collect informationglobally [10] and a powerful central controller to process hugeamounts of data. Thus, these solutions are costly to implementand susceptible to single-point failures. Due to the intermittencyof renewable generation, more frequent control updates arerequired. The centralized solutions may not be able to respondin a timely fashion if operating conditions change rapidly andunexpectedly.This paper targets small-scale, self-contained, medium

voltage microgrid power systems, which are composed ofmultiple RGs, a reliable synchronous generator (SG), andloads. For a microgrid to work autonomously, it must maintainits own supply-demand balance in term of active power andregulate the system frequency and voltage magnitudes. As theDGs within a microgrid could be diverse and distributed, thecontrol and management solutions should be as efficient andcost-effective as possible for the microgrid to be economicallyviable. Since well-designed distributed control solutions canbe flexible, reliable, scalable, and low-cost to implement [10],thus they are promising choice for the control and operation ofmicrogrids.Multi-agent system (MAS) is one of the most popular dis-

tributed control approaches in literature [11]–[14]. The conceptof MAS has been wide applied to various problems in micro-grid research, such as power management [12], distributed op-timization [13], active power and reactive power control [14].Existing MAS based applications in power systems are usuallyrule-based and lacked rigorous stability analysis. Recent devel-opments in consensus and cooperative control have been suc-cessfully applied [15]–[20], that can improve the stability andapplicability of MAS-based solutions.According to the MAS-based fully-distributed control solu-

tion presented in this paper, each RG controller has two controllevels. The upper control level implements a subgradient basedoptimization algorithm, which can maintain the supply-demandbalance by adjusting local utilization levels of RGs based on

local frequency measurement and maximum renewable powerprediction. Once the utilization level is updated, the referencefor local active power generation of the RGs can be calculatedand deployed by the lower control level. The DGs can be con-trolled either in voltage regulation mode or in reactive powercontrol mode. The control settings for different control modescan be decided locally according to operating conditions.In this paper, the coordination of multiple RGs in a micro-

grid is formulated as a convex optimization problem that can besolved using the distributed subgradient algorithm introduced in[21]–[23]. By adopting the near-optimal and stable coefficientssetting algorithm introduced in [15], [16], the convergence ofthe fully distributed MAS-based algorithm can be guaranteed.In addition, only local frequency measurement, predicted max-imum generation, and neighboring generators’ utilization levelsare needed to update local utilization level, which is realized bydesigning a control law based on the models of frequency dy-namics introduced in [24].The rest of the paper is organized as follows. Section II briefly

introduces conventional droop control. Section III describes theproposed control approach. Section IV introduces the machine-level control design. Section V presents simulation results withthe 6-bus microgrid. Finally, Section VI provides the conclusionand suggestions for future work.

II. CONVENTIONAL DROOP CONTROL

A microgrid can operate in either grid-connected mode or is-landed mode. In grid-connected mode, the microgrid can eitherinject power into, or absorb power from, the main grid. Thesupply-demand can be assumed to be balanced by the main gridmost of the time. In this scenario, each RG is controlled simplyto operate under the MPPT method. However, when a micro-grid operates in islanded mode, the supply-demand should bebalanced autonomously. Therefore, each component in the mi-crogrid should cooperate to achieve this goal.Droop control methods, which originate from the principle

of power balance of synchronous generators in large inter-connected power systems, are proposed to ensure good powersharing for a power grid [25], [26]. For convenience, the con-ventional droop control method is briefly introduced as follows.To maintain the frequency of an autonomous microgrid, the

active power outputs of each RG must be adjusted according topredefined droop characteristics [27] as

(1)

where and are the rated operating and locally-measuredfrequency of the microgrid, respectively; is the frequencydroop coefficient for RG ; is the initial active power gener-ation corresponding to ; and is the updated active powergeneration demand of RG .In a similar manner, the reactive power of each RG can be

adjusted according to the predefined droop characteristicsas

(2)

where and are the rated and measured voltage magni-tudes, respectively; is the voltage droop coefficient for RG

XU et al.: DISTRIBUTED SUBGRADIENT-BASED COORDINATION OF MULTIPLE RENEWABLE GENERATORS IN A MICROGRID 25

; is the initial reactive power generation corresponding to; and is the output reactive power reference of RG .The primary advantage of droop control is that it does not

require direct communication between DER units. However,conventional droop controllers have several drawbacks, suchas voltage and frequency deviations, inaccurate power sharing,and unsatisfactory transient performances, as summarizedin [27]–[34]. To overcome the problems with droop control,mainly the frequency deviation, automatic generation control(AGC) can be applied to adjust the generation referencesperiodically.

III. PROPOSED SUBGRADIENT-BASED SOLUTION

This section introduces the proposed fully-distributed algo-rithm, which can achieve the system’s power supply-demandbalance within the microgrid.

A. Utilization Level Based Coordination

The total active power demand of a microgrid can becalculated as

(3)

where is the number of buses in the microgrid, is thedemand of load at bus , and is the active power loss inthe microgrid.The total available renewable power generation in the micro-

grid can be calculated as

(4)

where is the number of RGs, and is the maximumpower generation of RG .In an autonomous microgrid, if is less than , all RGs

will operate in MPPT mode, and the SG(s) should compensatethe generation deficiency. On the other hand, if is largerthan , MPPT control strategies no longer apply. A suitabledeloading strategy is required to share the load demands amongthe RGs, which can be accomplished by controlling the utiliza-tion levels ( s) of RGs to a common value

(5)

where is the common utilization level for all RGs.The active power generation reference of RG is cal-

culated as

(6)

According to (4) and (6), it can be easily verified that thesupply-demand balance can be guaranteed when the maximumavailable renewable generation exceeds the load demand, as

(7)

B. Distributed Generation Coordination Algorithm

In an autonomous microgrid, to ensure static stability, thesupply and demand balance must be maintained. The objectivefor multiple RGs coordination is to minimize the function for-mulated as

(8)

where is the discrete time step, is the utilization level ofRG at step .This convex optimization problem can be solved using dis-

tributed subgradient algorithm. According to [21]–[23],can be updated according to

(9)

where is the communication coefficient, is the step size,and can be calculated as

(10)

If the communication system for the RG agents is repre-sented using a graph, the communication links between agentsare un-directional, i.e., . As discussed in the authors’previous work [15], different methods for determinationprovide different converging speeds. Since themean metropolisalgorithm as shown in (11) is fully distributed, adaptive tochanges of communication network topology, and able toprovide convergence guarantee and near optimal convergingspeed, it is adopted in this paper:

(11)

where and are the numbers of agents connected to agentsand , respectively, is the indices of agents that communicatewith agent .Substituting (10) into (9) yield

(12)By defining a dimensional communication coefficient ma-

trix composed of s, the overall updating process of theutilization levels in (12) can be represented using matrix form

(13)

with

26 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 1, JANUARY 2014

According to the mean metropolis algorithm, the transitionmatrix is a doubly stochastic matrix, which has the followingproperties:1) All the eigenvalues of are less or equal to 1.2) , , and , where

, .According to the Perron-Frobenius theorem [35], the transi-

tion matrix satisfies: .As discussed in [22], a distributed subgradient algorithm will

converge under two conditions. First, the transition matrixsatisfies: . Second, the step sizes sare sufficiently small. Since the designed transition matrix sat-isfies the first condition automatically and can be tuned smallenough by trial and error for this application, the convergenceof the proposed distributed subgradient based generation coor-dination algorithm can be guaranteed.The equilibrium of the system described by (13) can be ob-

tained by summing up both sides of (12) and letting, for

(14)According to (11), is a symmetric matrix with the sums of

each equals 1, i.e. . The first term of right handside of (14) can be calculated as

(15)Since , thus

(16)

Substituting (16) into (13) with yields

(17)

where .According to [36], the solution to (17) has the following form:

(18)

By substituting (18) into (16), when the system reaches itssteady state, the common utilization level can be determinedas

(19)

Therefore, the proposed control law can achieve the supply-demand balance within the microgrid according to (7).Measuring the total load and estimating power loss accurately

in a distributed way are difficult. Considering the fact that anysupply-demand imbalance will be reflected in changes of systemfrequency, it is intuitive to use frequency deviation to overcomethe difficulty.

The following model for dynamic frequency response is pro-posed in [24]:

(20)

where is the nominal frequency and is the initial kineticenergy of the generators, which is decided by the capacity of apower system [24].Equation (20) can be discretized according to

(21)

where is the time step for utilization level update.Therefore

(22)

By substituting (22) into (12), finally the proposed updatinglaw for the utilization level of RG can be represented as

(23)

where .It should be noted that it is unnecessary to estimate ,

which changes with operating conditions and is hard to accu-rately estimate. Since its impact on control update has been com-bined with the other parameters and absorbed into . Thus, itis preferable and reasonable to tune directly.For a specific operating condition, can be identified by trial

and error method. Since smaller usually results in slower con-vergence, larger is preferable. However, large might causesystem instability. To achieve a good balance between stabilityand convergence, can be initialized with a reasonably smallvalue, such as the 0.1 used for the simulated system. After that,the value of is kept increasing at a small step size of 0.02 untildivergence, which corresponds to stability margin. Half of thethat starts to cause instability is selected as the final value.

The value of selected for the simulated system is 0.24.

C. Algorithm Implementation

The proposed control topology is shown in Fig. 1, which ismainly composed of RGs, an SG and loads.Each RG is assigned an RG agent. An RG agent can measure

the system’s frequency, predict its maximum renewable powergeneration, and exchange information with its neighboringagents. The supporting communication system for the MASbased solutions can be designed to be independent to thetopology of the power network. Even for a complex system,simple communication network can be designed base on cost,location, convenience, etc. Each SG is assigned an SG agent,which does not participate in the utilization level updatingprocess. The SG agent decides the control mode of the SGthrough control mode selection (CMS), which will be intro-duced in Section IV.

XU et al.: DISTRIBUTED SUBGRADIENT-BASED COORDINATION OF MULTIPLE RENEWABLE GENERATORS IN A MICROGRID 27

Fig. 1. Illustration of the control topology of a microgrid.

Fig. 2. Block diagram of operations of an RG agent.

The operation of an RG agent is shown in Fig. 2. Each gen-erator agent implements a two-level control strategy. The uppercooperative level control (CLC) discovers the desired utiliza-tion level and decides the reference of active power genera-tion. The CLC consists of four function modules. The measure-ment and prediction module measures the system’s frequencyand predicts the maximum available renewable generation. Thecommunication module exchanges utilization level informationwith its neighboring RG agents. Based on local frequency devia-tionmeasurements and received utilization levels, the utilizationlevel will be updated according to (23). The active power gener-ation reference is then calculated based on the utilization leveland the predicted maximum renewable power. The lower ma-chine control (MLC) level realizes active power tracking whilesatisfying other requirements regarding reactive power and ter-minal voltage regulation.According to the proposed distributed algorithm, there is

no need to measure global loading conditions and losses inthe system. Since any supply demand imbalance will result inchanges in frequency, the utilization level of an RG can be ad-justed based on measured frequency deviation as shown in (23).In this way, the amount of measurements can be significantlyreduced. In addition, the complexity and cost of the supportingcommunication network can also be lowered.The maximum active power generation of a DFIG can be es-

timated using measured wind speed [37]. In addition, there aremany other MPPT algorithms for wind turbine generators avail-able in literature, as summarized in [38]. Similarly, the max-imum generation of a PV generator can be predicted based onweather condition (solar insolation, temperature, etc.) [39]. A

Fig. 3. Machine-level control of DFIG in deloading mode.

lot of MPPT algorithms for PV generators have been developedin the past years [40], such as, fuzzy logic control, neural net-work, etc.Inaccuracy of the maximum power estimation always exists

to some extend due to the prediction errors [41]. Sometimes thepredicted value is larger than practical, sometimes smaller. Forunder-estimation, the predicted generation can be realized. Forover-estimation, such as due to the aging problem or internalfailures of a PV system, the advantage of the proposed algorithmwill present. The proposed algorithm updates generation refer-ences based on overall generation estimations and overall de-mand. Since the generation reference settings are usually lowerthan the under sufficient renewable generation, the impactof inaccurate estimation can be lowered.

IV. CONTROL OF DIFFERENT TYPES OF DGS

A. Control of DFIG

The machine-level control of each DFIG manages activepower reference tracking, as well as reactive power or ter-minal voltage regulation and DC-link voltage regulation. Asillustrated in Fig. 3, the machine-level control consists of theelectrical control of two converters and the mechanical controlof pitch angle.A typical DFIG model introduced in [42] is adopted in this

paper. The active power generation of the DFIG can be regu-lated by controlling rotor speed and/or tuning pitch angle[40]. The former method is preferred for two reasons. First, iscontrolled by converter control, whose response speed is fasterthan the mechanical pitch angle control. Second, electrical con-trol of can decrease wear and tear on the pitch blade. How-ever, when the rotor speed reaches the upper bound, it is nec-essary to activate the pitch angle tuning. The implementationdetails of DFIG control are presented in [17].1) Converter Control: In this paper, the DFIG is controlled

by back-to-back converters. With the decoupled control methodintroduced in [43], the rotor-side converter (RSC) controls boththe active and reactive power of the DFIG. The active poweris controlled by adjusting the -axis rotor current , while thereactive power is controlled by adjusting the -axis rotor current, as shown in Fig. 4.The deviation between the active power output of DFIG

and the reference value forms the error signal that is pro-cessed by a PI controller to produce the rotor current reference. Through another PI controller, the difference between rotor

28 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 1, JANUARY 2014

Fig. 4. Schematic diagram of control strategy for RSC and GSC of a DFIG.

Fig. 5. Pitch angle control system.

current and reference value is used to produce rotorvoltage .There are two modes for reactive power control, the voltage

and reactive power regulation modes. Both modes regulateq-axis rotor current . In voltage regulation mode, is con-trolled to reduce voltage fluctuation [44]. For reactive powerregulation, the difference between the reactive commandand the reactive power output forms rotor current referencethrough a PI controller.Here, GSC is used only to stabilize the DC-link voltage. More

details can be found in [45] and [46].2) Pitch Angle Control: The pitch angle control method, as

depicted in Fig. 5, consists of a PI controller and a pitch angle ac-tuator. The threshold speed is set to 1.3 p.u., and is set to 0.The maximum pitch angle change rate is limited byand .

B. PV Control

The PV system model described in [47] is adopted in thispaper. and are the solar array voltage and current, respec-tively, and and are the local bus voltage and current.In this paper, PV is controlled in unit power factor mode. If aPV system is equipped with insolation and temperature sensors,the following method introduced in [48] can be used to estimatethe maximum generation of :

(24)

Fig. 6. Control strategy for PV system.

Fig. 7. Control logic of synchronous machine.

where is the module maximum power at standard testcondition (STC), is the incident irradiance, is irra-diance at STC 1000 , is the temperature coefficientof power, and and are the cell temperature and the refer-ence temperature (25 ), respectively.Once and have been calculated, the generation ref-

erence can be updated according to (6). After that, simplePI control can be used to control the inverters for active powertracking, as shown in Fig. 6.

C. Control of SG

In this paper, the SG in the renewable microgrid has two func-tions. If the renewable generation is sufficient to power all loads,SG is just used for voltage regulation. If the renewable gener-ation is insufficient, in addition to voltage regulation, the SGalso generates active power to compensate the deficiency. TheSG does not need to participate in the discovery of desired uti-lization level. The SG agent can monitor the instantaneous uti-lization level of one of its nearby RGs in order to determine itscontrol mode through CMS, as shown in Fig. 7. If the utilizationlevel equals to 1 and the frequency deviation is negative, the SGwill generate active power to compensate the deficiency of therenewable generation. Otherwise, the SG will only provide re-active power support to maintain local voltage level.A rate limiter is used to model the ramp rate of the

SG in the control loop. The governor system is modeled as aPI controller, as described in [49]. The excitation system blockadopts a DC exciter, as recommended in [50].

V. SIMULATION STUDIES

The proposed fully-distributed cooperative control al-gorithm is tested with a 6-bus microgrid model usingMATLAB/SIMULINK, as shown in Fig. 8. The systemcontains six loads, three DFIGs, two PVs and one SG. TheDFIG at bus-1 (abbreviated as DFIG-1) is controlled in reactivepower regulation mode, the DFIG-4 and DFIG-5 are controlled

XU et al.: DISTRIBUTED SUBGRADIENT-BASED COORDINATION OF MULTIPLE RENEWABLE GENERATORS IN A MICROGRID 29

Fig. 8. Configuration of a 6-bus microgrid.

Fig. 9. Communication topology of the MAS for 6-bus microgrid.

Fig. 10. Utilization level profiles of 5 RGs (Test 1).

in voltage regulation mode, and the PV-2 and PV-3 are con-trolled in unit power factor mode, as introduced in Section IV.The ramp-up and ramp-down rates of the SG are both set to 0.4MW/s. The communication topology of the MAS for the 6-busmicrogrid is as shown in Fig. 9.During simulations, time step for utilization level update is

selected to be 0.1 s, which has good balance of control perfor-mance and technical feasibility. The proposed control strategyis tested under two operating conditions. Test 1 establishes aconstant available renewable generation and loads. Test 2 has avariable available renewable generation and loads. The first testis unrealistic yet easier to understand due to its simplicity.

A. Test 1

In the first test, the demands of the loads remain constant.The wind speeds of the DFIGs at bus-1, bus-4, and bus-5 areconstant at 11 m/s, 14 m/s, and 14 m/s, respectively. The solarinsolation of PVs at bus-2 and bus-3 are 900 and 1000

, respectively. An islanding event at 20 s is simulated totest the performance of the proposed control strategy.Fig. 10 shows the utilization level profile. Before islanding,

RGs are controlled using the MPPT algorithm, and the initialoutput of the SG is set to 2 MW to create enough disturbancesto test the performance of the proposed control algorithm. Atthe instant of islanding, the available renewable power is morethan the load demand, the system’s frequency increases at thismoment as shown in Fig. 12. The proposed algorithm forcesthe utilization level to drop in order to allow the RGs to dumpexcessive renewable power.

Fig. 11. Dynamic response of DGs. (a) DFIG-1 active power output; (b) PV-2active power output; (c) PV-3 active power output; (d) DFIG-4 active poweroutput; (e) DFIG-5 active power output.

Fig. 12. System response under the proposed solution. (a) Frequency response;(b) terminal voltages of DGs.

Fig. 11 shows the dynamic responses of the RGs. The ac-tive power generations of the DGs converge to a value belowthe maximum available power after islanding. The utilizationlevels, if calculated, are the same as the ratio of actual outputpower to MPPT power.To evaluate the performance of the proposed algorithm, the

traditional Droop-AGC method is simulated for comparison.Droop control is used to adjust the generations based on prede-fined P-f Q-V characteristic. AGC is applied every 5 s to elimi-nate frequency deviation. The dynamic responses under the pro-posed algorithm and Droop-AGC method are shown in Figs. 12and 13, respectively.By comparing Figs. 12(a) and 13(a), one can see that the

frequency response under the proposed solution is able toconverge to the nominal value within 6 s, while it takes theDroop-AGC method 30 s to converge. In addition, the over-shoot of frequency response under the proposed algorithmis 0.19 Hz, which is much smaller than that of the conven-tional droop method (0.32 Hz). Similar observations can bemade for voltage responses under the proposed algorithmand Droop-AGC method, as shown in Figs. 12(b) and 13(b),respectively. The improved performance comes from dynamicand accurate generation adjustments as compared to using fixedP-f and Q-V characteristics.

30 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 1, JANUARY 2014

Fig. 13. System response under the Droop-AGC method. (a) Frequency re-sponse; (b) terminal voltages of DGs.

Fig. 14. Wind speed and solar insolation profiles of the RGs.

Test 1 is conducted under constant renewable generations.Under such conditions, it is possible to select suitable valuesfor and in (1) and (2). Due to its simplicity, this testis conducted here to give preliminary introduction of the pro-posed solution. Since the maximum generations of the RGs areassumed to be constants, the RGs act like traditional SGs. Basedon the simulation results, it can be concluded that the algorithmproposed in the paper can also be applied to coordinate multipleSGs in a traditional power system and the performance will bebetter than that of traditional Droop-AGC controls.However, because of the intermittency and unreliability of re-

newable energy resources, the maximum generations of RGs areusually time-varying. To achieve accurate power sharing, thedroop control parameters, and , need to be adjusted dy-namically based on instantaneous operating conditions, whichis hard to realize. In addition, even if the periodical AGC can beapplied much faster than current practice of 10 s or longer [51],[52], such as the 5 s adopted in simulation, it still might be in-sufficient for autonomous renewable microgrid that has reducedinertia. Thus, Droop-AGC is not simulated in the following testunder variable renewable generation.

B. Test 2

The wind speed and solar insolation profiles of differentDFIGs and PVs in the second test are shown in Fig. 14. Inthis test, the initial output of the SG is intentionally set to 4MW. The sequence of events in this simulation consists of themicrogrid being isolated from the main grid at 60 s, and then aload of 2 MW being shed at 150 s and restored at 200 s.As shown in Fig. 15, the proposed algorithm is good at co-

ordinating the utilization level of five RGs to a common value.The utilization level drops below 1 immediately after grid dis-connection. The SG switches to voltage regulation mode and itsactive power generation gradually decreases from 4MW to zero

Fig. 15. Utilization level profiles of 5 RGs (Test 2).

Fig. 16. Maximum generation and total load demand profiles.

according to the pre-defined ramp-down rate. At 150 s, a loadof 2 MW is shed, and the utilization level drops so that the RGscan reduce the renewable generation. The utilization level risesat 200 s when the load is restored. When the estimated max-imum renewable generation is insufficient, the utilization levelreaches the upper bound and is capped at 1, and all of the RGsare controlled in MPPT mode, which can be observed duringthe period from 228 s to 300 s. Meanwhile, the SG is controlledto generate active power to compensate for the deficiency, asshown in Fig. 19.To illustrate the dynamic performance of the utilization

level, the available total renewable generation and total loadprofiles are plotted together in Fig. 16. When the loads aremodeled as serial RLC modules with constant parameters, theactual load will oscillate due to frequency and voltage fluc-tuations. This phenomenon can be observed when operatingconditions change in Fig. 16. Investigating the responses of thefrequency and terminal voltages (Fig. 20) helps to clarify thisphenomenon.Fig. 17 shows the utilization level, the actual active power

generation, and the available maximum wind power of DFIG-4.DFIG-4 can operate in deloading mode when the available re-newable power exceeds the demand (60 s–228 s) and in MPPTmode when the available maximum renewable power is insuf-ficient (228 s–300 s). Similar performances can be observed forother RGs, which are not shown here.The rotor speed and pitch angle responses of DFIG-4 are

shown in Fig. 18. When the rotor speed is below the thresholdof 1.3 p.u., the pitch angle control is not activated and remainsat . Pitch angle control is activated when the rotor speedreaches the upper limit.Fig. 19 shows the active and reactive power generation of the

SG. At the instant of islanding at 60 s, the active power gener-ation of the SG is gradually reduced to 0 because the availablerenewable generation is more than the total load demand. The

XU et al.: DISTRIBUTED SUBGRADIENT-BASED COORDINATION OF MULTIPLE RENEWABLE GENERATORS IN A MICROGRID 31

Fig. 17. Active power tracking of DFIG-4.

Fig. 18. Rotor speed and pitch angle of DFIG-4.

Fig. 19. Active and reactive power of the SG.

decreasing slope of active power generation is decided by theramp rates of the SG. When there is insufficient renewable gen-eration ( and frequency deviation is negative), the SG iscontrolled to generate active power to compensate for insuffi-cient power during 228 s to 300 s.The frequency and voltage responses are usually customers’

main concerns, and they should be evaluated by up-to-datestandards and regulation codes. According to the IEEE Std.1547 [53], the normal frequency should be within the rangeof 59.8 Hz–60.5 Hz. ANSI/NEMA C84.1 [54] recommendsthat the frequency deviation should be within 0.05 Hz andthe voltage within 0.90 p.u.–1.10 p.u. Fig. 20 indicates thatthe maximum frequency deviation (60.4 Hz) is less than 60.5Hz, and the voltage response is in the range of (0.96 p.u.–1.05p.u.). Therefore, both the frequency and voltage performancesmeet the above standards. During the simulation study, DFIG-4and DFIG-5 are operated in voltage regulation mode, and theSG, DFIG-1, PV-2 and PV-3 are operated in reactive powergeneration mode. In the latter mode, a fixed amount of reactivepower is generated, and there is no direct control of the terminalvoltage. This is why the terminal voltage responses of buses involtage regulation mode are much better than those of the otherbuses.

Fig. 20. System response of test 2. (a) System frequency response; (b) terminalvoltages of DGs.

VI. CONCLUSION

This paper targets at the coordination problem with anautonomous microgrid under high penetration of renewableenergy. Two main reasons motivate the authors to controlthe utilization level to a common value instead of controllingsome RGs in MPPT mode and others in reduced generationmode. First, MPPT algorithms that emphasize high renewableenergy utilization may cause supply-demand imbalance whenthe available renewable generation is more than demanded.Second, every MPPT algorithm has the problem of imprecise-ness to certain degree and the predicted maximum availablegeneration might be unachievable. By synchronizing the uti-lization levels of the RGs to a common value, the impactsof prediction impreciseness of the MPPT algorithms can beefficiently mitigated.The proposed control scheme has the following four main

advantages. The first advantage is the introduction of a simpleMAS-based fully distributed method. Due to the simplicity ofthe network topology and the reduced amount of information toexchange, the cost of the supporting communication networkwill be much lower than that of a centralized solution. Thesecond is its avoidance of the direct measurements of loadingconditions. The third is its distributed coordination of differenttypes of DGs (DFIG, PV, and SG), which can maintain thesupply-demand balance within the microgrid. The fourth is itsintroduction of the subgradient optimization method, which im-proves the system’s dynamic performance. Simulation studiesdemonstrate that the multiple RGs and the SG are well coor-dinated to maintain the power supply-demand balance for theautonomous microgrid in both excessive and insufficient avail-able renewable power situations.

REFERENCES[1] S. Abu-Sharkh, R. J. Arnold, J. Kohler, and R. Li, “Can microgrids

make a major contribution to UK energy supply?,” Renew. Sustain.Energy Rev., vol. 10, no. 2, pp. 78–127, 2006.

[2] A.Mehrizi-Sani, A. H. Etemadi, D. E. Olivares, and R. Iravani, “Trendsin microgrid control,” IEEE Trans. Smart Grid, to be published.

32 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 1, JANUARY 2014

[3] N. Femia, G. Petrone, G. Spagnuolo, and M. Vitelli, “Optimization ofperturb and observe maximum power point tracking method,” IEEETrans. Power Electron., vol. 20, no. 4, pp. 963–973, 2005.

[4] E. Koutroulis and K. Kalaitzakis, “Design of a maximum powertracking system for wind-energy-conversion applications,” IEEETrans. Ind. Electron., vol. 53, no. 2, pp. 486–494, 2006.

[5] L. Qu and W. Qiao, “Constant power control of DFIG wind turbineswith supercapacitor energy storage,” IEEE Trans. Ind. Applicat., vol.47, no. 1, pp. 359–367, 2011.

[6] J. L. Rodriguez-Amenedo, S. Arnalte, and J. C. Burgos, “Automaticgeneration control of a wind farm with variable speed wind turbines,”IEEE Trans. Energy Convers., vol. 17, no. 2, pp. 279–284, 2002.

[7] R. G. de Almeida, E. D. Castronuovo, and J. A. P. Lopes, “Optimumgeneration control in wind parks when carrying out system operatorrequests,” IEEE Trans. Power Syst., vol. 21, no. 2, pp. 718–725, May2006.

[8] L. R. Chang-Chien, C. M. Hung, and Y. C. Yin, “Dynamic reserveallocation for system contingency by DFIG wind farms,” IEEE Trans.Power Syst., vol. 23, no. 2, pp. 729–736, May 2008.

[9] T. Senjyu, A. Yona, M. Datta, H. Sekine, and T. Funabashi, “Acoordinated control method for leveling output power fluctuations ofmultiple PV systems,” in Proc. Int. Conf. Power Electronics, 2007,pp. 445–450.

[10] H. Xin, Z. Qu, J. Seuss, and A. Maknouninejad, “A self-organizingstrategy for power flow control of photovoltaic generators in a distribu-tion network,” IEEE Trans. Power Syst., vol. 26, no. 3, pp. 1462–1473,Aug. 2011.

[11] A. Dimeas and N. Hatziargyriou, “A multiagent system for micro-grids,” in Proc. IEEE Power Engineering Society General Meeting,2004, vol. 1, pp. 55–58.

[12] C. M. Colson and M. H. Nehrir, “Algorithms for distributed decision-making for multi-agent microgrid power management,” in Proc. 2011IEEE Power and Energy Society General Meeting, 2011, pp. 1–8.

[13] B. Zhao, C. X. Guo, and Y. J. Cao, “A multiagent-based particleswarm optimization approach for optimal reactive power dispatch,”IEEE Trans. Power Syst., vol. 20, no. 2, pp. 1070–1078, May 2005.

[14] A. L. Kulasekera, R. A. R. C. Gopura, K. T. M. U. Hemapala, and N.Perera, “A review on multi-agent systems in microgrid applications,”in Proc. 2011 IEEE PES Innovative Smart Grid Technologies, 2011,pp. 173–177.

[15] Y. Xu andW. Liu, “Novel multi agent based load restoration algorithmfor microgrids,” IEEE Trans. Smart Grid, vol. 2, no. 1, pp. 140–149,2011.

[16] Y. Xu, W. Liu, and J. Gong, “Multi-agent based load shedding algo-rithm for power systems,” IEEE Trans. Power Syst., vol. 26, no. 4, pp.2006–2014, Nov. 2011.

[17] W. Zhang, Y. Xu, W. Liu, F. Ferrese, and L. Liu, “Fully distributedcoordination of multiple DFIGs in a microgrid for load sharing,” IEEETrans. Smart Grid, to be published.

[18] F. Ferrese et al., “Cooperative federated control with application totracking control,” in Proc. 2011 IEEE 13th Int. Conf. High Perfor-mance Computing and Communications (HPCC), 2011.

[19] Q. Dong, K. Bradshaw, F. Ferrese, L. Bai, and S. Biswas, “Coopera-tive federated multi-agent control of large-scale systems,” Control Ap-plicat., 2011.

[20] S. Biswas, F. Ferrese, Q. Dong, and L. Bai, “Resilient consensus con-trol for linear systems in a noisy environment,” inProc. IEEEAmericanControl Conf. (ACC), 2012, Jun. 2012, pp. 5862–5867.

[21] L. Xiao and S. Boyd, “Optimal scaling of a gradient method for dis-tributed resource allocation,” J. Optimiz. Theory Applicat., vol. 29, no.3, pp. 469–488, 2006.

[22] A. Nedic and A. Ozdaglar, “Distributed subgradient methods for multi-agent optimization,” IEEE Trans. Autom. Control, vol. 54, no. 1, pp.48–61, 2009.

[23] I. Lobel and A. Ozdaglar, “Distributed subgradient methods for convexoptimization over random networks,” IEEE Trans. Autom. Control, vol.56, no. 6, pp. 1291–1306, 2011.

[24] J. W. O’Sullivan and M. J. O’Malley, “Identification and validationof dynamic global load model parameters for use in power systemfrequency simulations,” IEEE Trans. Power Syst., vol. 11, no. 2, pp.851–857, May 1996.

[25] M. C. Chandorkar and D. M. Divan, “Control of parallel connectedinverters in standalone AC supply system,” IEEE Trans. Ind. Applicat.,vol. 29, no. 1, pp. 136–143, 1993.

[26] S. J. Chiang and J. M. Chang, “Parallel control of the UPS inverterswith frequency-dependent droop scheme,” in Proc. 2001 IEEE 32ndAnnual Power Electronics Specialists Conf., 2001, vol. 2, pp. 957–961.

[27] F. Katiraei and M. R. Iravani, “Power management strategies for a mi-crogrid with multiple distributed generation units,” IEEE Trans. PowerSyst., vol. 21, no. 4, pp. 1821–1831, Nov. 2006.

[28] J. He and Y. W. Li, “Analysis, design and implementation of virtualimpedance for power electronics interfaced distributed generation,”IEEE Trans. Ind. Applicat., vol. 47, no. 6, pp. 2525–2538, 2011.

[29] W. Yao, M. Chen, J. Matas, J. M. Guerrero, and Z. Qian, “Design andanalysis of the droop control method for parallel inverters consideringthe impact of the complex impedance on the power sharing,” IEEETrans. Ind. Electron., vol. 58, pp. 576–588, 2011.

[30] J. M. Guerrero, J. C. Vásquez, J. Matas, M. Castilla, L. G. D. Vicuña,and M. Castilla, “Hierarchical control of droop-controlled AC and DCmicrogrids—A general approach toward standardization,” IEEE Trans.Ind. Electron., vol. 58, pp. 158–172, 2011.

[31] M. B. Delghavi and A. Yazdani, “An adaptive feed-forward compensa-tion for stability enhancement in droop-controlled inverter-based mi-crogrids,” IEEE Trans. Power Del., vol. 26, no. 3, pp. 1764–1773,2011.

[32] Y. Mohamed and E. F. El-Saadany, “Adaptive decentralized droopcontroller to preserve power sharing stability of paralleled inverters indistributed generation microgrids,” IEEE Trans. Power Electron., vol.23, no. 6, pp. 2806–2816, Nov. 2008.

[33] N. R. Chaudhuri and B. Chaudhuri, “Adaptive droop control for effec-tive power sharing in multi-terminal DC (MTDC) grids,” IEEE Trans.Power Syst., 2012, to be published.

[34] A. Bidram and A. Davoudi, “Hierarchical structure of microgrids con-trol system,” IEEE Trans. Smart Grid, 2012, to be published.

[35] R. Olfati-Saber, J. Fax, and R. Murray, “Consensus and cooperationin networked multi-agent systems,” Proc. IEEE, vol. 95, no. 1, pp.215–233, Jan. 2007.

[36] Z. Qu, Cooperative Control of Dynamical Systems: Applications to Au-tonomous Vehicles. London, U.K.: Springer Verlag, 2009.

[37] A.M. Foley, P. G. Leahy, and E. J. McKeogh, “Wind power forecasting& prediction methods,” in Proc. 2010 9th Int. Conf. Environment andElectrical Engineering, 2010, pp. 61–64.

[38] M. Lydia and S. S. Kumar, “A comprehensive overview on wind powerforecasting,” in Proc. IPEC, 2010 Conf., 2010, pp. 268–273.

[39] N. Femia, G. Petrone, G. Spagnuolo, and M. Vitelli, “Optimization ofperturb and observe maximum power point tracking method,” IEEETrans. Power Electron., vol. 20, no. 4, pp. 963–973, 2005.

[40] T. Esram and P. L. Chapman, “Comparison of photovoltaic array max-imum power point tracking techniques,” IEEE Trans. Energy Convers.,vol. 22, no. 2, pp. 439–449, 2007.

[41] A. B. G. Bahgat, N. H. Helwa, G. E. Ahamd, and E. T. El Shenawy,“Estimation of the maximum power and normal operating power of aphotovoltaic module by neural networks,” Renew. Energy, vol. 29, no.3, pp. 443–457, 2004.

[42] S. Heier, Grid Integration of Wind Energy Conversion Sys-tems. Chicester, U.K.: Wiley, 1998.

[43] A. Luna, F. K. de Araujo Lima, D. Santos, P. Rodriguez, E. H.Watanabe, and S. Arnaltes, “Simplified modeling of a DFIG for tran-sient studies in wind power applications,” IEEE Trans. Ind. Electron.,vol. 58, no. 1, pp. 9–20, Jan. 2011.

[44] O. Anaya-Lara, N. Jenkins, J. Ekanayake, P. Cartwright, and M.Hughes, Wind Energy Generation: Modeling and Control. NewYork, NY, USA: Wiley, 2009.

[45] R. P. S. Chandrasena, A. Arulampalam, J. B. Ekanayake, and S. G.Abeyratne, “Grid side converter controller of DFIG for wind powergeneration,” in Proc. Int. Conf. Industrial and Information Systems(ICIIS 2007), Aug. 9–11, 2007, pp. 141–146.

[46] E. Tremblay, A. Chandra, P. J. Lagace, and R. Gagnon, “Study of grid-side converter control for grid-connected DFIG wind turbines underunbalanced load condition,” in Proc. 2006 IEEE Int. Symp. IndustrialElectronics, Jul. 9–13, 2006, vol. 2, pp. 1619–1624.

[47] M. Datta, T. Senjyu, A. Yona, T. Funabashi, and C. H. Kim, “A co-ordinated control method for leveling PV output power fluctuations ofPV-diesel hybrid systems connected to isolated power utility,” IEEETrans. Energy Convers., vol. 24, no. 1, pp. 153–162, 2009.

[48] F. A. Mohamed and H. N. Koivo, “Online management of microgridwith battery storage using multi-objective optimization,” in Proc. Int.Conf. Power Engineering, Energy and Electrical Drives, 2007, pp.231–236.

[49] IEEE Committee Report, “Dynamic models for steam and hydro tur-bines in power system studies,” IEEE Trans. Power App. Syst., vol.PAS-92, no. 6, pp. 1904–1915, 1973.

[50] Recommended Practice for Excitation System Models for PowerSystem Stability Studies, IEEE Std. 421.5-1992, Aug. 1992.

XU et al.: DISTRIBUTED SUBGRADIENT-BASED COORDINATION OF MULTIPLE RENEWABLE GENERATORS IN A MICROGRID 33

[51] B. Kirby and E. Hirst, “Generator response to intrahour load fluctua-tions,” IEEE Trans. Power Syst., vol. 13, no. 4, pp. 1373–1378, Nov.1998.

[52] N. Jaleeli, D. N. Ewart, and L. H. Fink, “Understanding automatic gen-eration control,” IEEE Trans. Power Syst., vol. 7, no. 3, pp. 1106–1122,Aug. 1992.

[53] IEEE Standard for Interconnecting Distributed Resources With Elec-tric Power Systems, IEEE Std. 1547-2003, 2003, pp. 1–27.

[54] American National Standard for Electric Power Systems and Equip-ment-Voltage Ratings (60 Hertz), ANSI C84.1-2006.

Yinliang Xu (S’10) received the B.S. and M.S.degrees in control science and engineering fromHarbin Institute of Technology, Harbin, China,in 2007 and 2009, respectively. Currently, he ispursuing the Ph.D. degree at the Klipsch Schoolof Electrical and Computer Engineering of NewMexico State University, Las Cruces, NM, USA.His research interests include intelligent control

and optimization of microgrids.

Wei Zhang (S’11) received the B.S. and M.S. de-grees in power system engineering fromHarbin Insti-tute of Technology, Harbin, China, in 2007 and 2009,respectively. Currently, he is pursuing the Ph.D. de-gree at the Klipsch School of Electrical and Com-puter Engineering of New Mexico State University,Las Cruces, NM, USA.His research interests include distributed control

and optimization of power systems, renewable en-ergy and power system state estimation and stabilityanalysis.

Wenxin Liu (S’01–M’05) received the B.S.and M.S. degrees from Northeastern University,Shenyang, China, in 1996 and 2000, respectively,and the Ph.D. degree in electrical engineering fromthe Missouri University of Science and Technology(formerly University of Missouri-Rolla), Rolla, MO,USA, in 2005.From 2005 to 2009, he was an Assistant Scholar

Scientist with the Center for Advanced Power Sys-tems of Florida State University. He is currently anAssistant Professor with the Klipsch School of Elec-

trical and Computer Engineering of New Mexico State University, Las Cruces,NM, USA. His research interests include power systems, control, computationalintelligence, and renewable energy.

Xin Wang received the B.S. degree in electricalengineering from Shanghai Jiao Tong University,Shanghai, China, in 1993, and the M.S. and Ph.D.degrees in control theory and engineering fromNortheastern University, Shenyang, China, in 1998and 2002, respectively.From 2002 to 2004, he was a Postdoctoral Re-

search Fellow in Shanghai Jiao Tong Universityand now he is an Associate Professor. His currentresearch interests include distributed generation,transmission, storage and forecasting technology of

renewable energy resource, distributed control and optimization of microgrid.

Frank Ferrese (M’04) received the B.S. degreein electrical engineering from Drexel University,Philadelphia, PA, USA, and the M.S. degree incomputer engineering from Villanova University,Philadelphia. He received the Ph.D. degree inengineering from Villanova University in 2013.He is a research engineer at Naval Surface Warfare

Center, Carderock Division, West Bethesda, MD,USA. He currently does research in the area ofcontrols and automation.

Chuanzhi Zang received the B.S. degree in appli-cation mathematics and the M.S. degree in controltheory and control engineering from NortheasternUniversity, Shenyang, China, in 1999 and 2002,respectively, and the Ph.D. degree in mechatronic en-gineering, Graduate School of the Chinese Academyof Sciences, Shenyang, China in 2006.He is an Associate Professor in Shenyang Insti-

tute of Automation, Chinese Academy of Sciences.His research interest include wireless sensor network,control theory and smart grid.

Haibin Yu (M’11) received the B.S., and M.S. de-grees in automation engineering and the Ph.D. degreein control theory and control engineering fromNorth-eastern University, Shenyang, China, in 1984, 1987,and 1997, respectively.He has more than 25 years of research experience

in fieldbus, industrial wireless network, wirelesssensor networks, network controlled systems, andnetwork manufacturing. He is currently the presidentand the professor of Shenyang Institute of Automa-tion (SIA), Chinese Academy of Sciences (CAS),

Shenyang, China. He focuses on the basic and applied research in the areas ofautomation control systems, advanced manufacture technique and smart grid.Dr. Yu is a Senior Member of the Instrumentation, Systems, and Automation

Society.